Implication
If two propositions and can be combined into statements of form: If p, then q, the statement is considered an implication.
Denoted by
Latex:
Let : it will rain tomorrow. : i will get wet if I go outside
If it will rain tomorrow, I will get wet if I go outside.
Since the statement contains a condition, it is called a conditional statement.
The component is the hypothesis (or premise) of the implication, and q is the conclusion.
Implications occur in a number of ways:
If p, then q If p, q p implies q p only if q q if p p is sufficient for q q is necessary for p
Note: only only if does not have the same mean ing as "p if q". "p if q" has the same meaning as "If q, then p"
Converse, contrapositive and inverse
Let and be propositions and the conditional statement
Converse
The proposition is the converse of A
Contrapositive
The proposition is the Contrapositive of A.
Inverse
The proposition is the inverse of A